Solve the problem.
-In a population of 240 women, the heights of the women are normally distributed with a mean of $64.2$ inches and a standard deviation of $3.2$ inches. If 36 women are selected at random, find the mean $\mu _ { \mathrm { x } } ^ { - }$and standard deviation $\sigma _ { \mathrm { x } } ^ { - }$of the population of sample means. Assume that the sampling is done without replacement and use a finite population correction factor.
A) $64.2$ inches, $0.49$ inches
B) $59.3$ inches, $2.96$ inches
C) $64.2$ inches, $3.2$ inches
D) $64.2$ inches, $1.88$ inches

Question

Quizplus · Accepted Answer

The mean of the sample means $\mu _ { \mathrm { x } } ^ { - }$ is equal to the population mean, which is $64.2$ inches. The standard deviation of the sample means $\sigma _ { \mathrm { x } } ^ { - }$ is calculated using the formula $\sigma _ { \mathrm { x } } ^ { - } = \frac{\sigma}{\sqrt{n}} \times \sqrt{\frac{N - n}{N - 1}}$, where $\sigma$ is the population standard deviation, $n$ is the sample size, and $N$ is the population size. Substituting the given values ($\sigma = 3.2$, $n = 36$, $N = 240$), we find $\sigma _ { \mathrm { x } } ^ { - } \approx 0.49$ inches.

Solve the Problem 64.264.264.2 Inches and a Standard Deviation Of 3.23.23.2 Inches If 36 Women Are Selected at Random, Find the Heights

Solve the Problem $64.2$ Inches and a Standard Deviation Of $3.2$ Inches If 36 Women Are Selected at Random, Find the Heights